Abstract
We study the negative-U Hubbard model by exact diagonalization of a 4\ifmmode\times\else\texttimes\fi{}4 cluster with different numbers of particles. We calculate the ground-state energy and wave function as well as the one-particle, charge- and spin-excitation spectra. We show that the BCS approximation gives results in good agreement with the exact ones for the ground-state energy and wave function in the whole range of U. In the one-particle excitation spectrum the BCS dispersion relation gives the position of the most intense peaks of the exact calculation. Lower-energy (quasiparticle) excitations, which are interpreted as strongly dressed Bogoliubov quasiparticles, also appear. The occurrence of pair-breaking and collective excitations in the charge- and spin-excitation spectra and the interplay between one-particle and collective modes are discussed.
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